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1Department of Physics and Astronomy, University of California, Irvine, CA 92697-4575, USA. 2Department of Physics, Incheon National University, Incheon 22012,Korea.*Corresponding author. Email: wur@uci.edu

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Magnetizing topological surface states of Bi2Se3 with aCrI3 monolayerYusheng Hou1, Jeongwoo Kim1,2, Ruqian Wu1*

To magnetize surfaces of topological insulators without damaging their topological feature is a crucial step forthe realization of the quantum anomalous Hall effect (QAHE) and remains as a challenging task. Through densityfunctional calculations, we found that adsorption of a semiconducting two-dimensional van der Waals (2D-vdW)ferromagnetic CrI3 monolayer can create a sizable spin splitting at the Dirac point of the topological surface statesof Bi2Se3 films. Furthermore, general rules that connect different quantum and topological parameters areestablished through model analyses. This work provides a useful guideline for the realization of QAHE at hightemperatures in heterostructures of 2D-vdW magnetic monolayers and topological insulators.

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INTRODUCTIONTopological insulators (TIs) are emergent quantummaterials that havenontrivial bandgaps in their bulks along with topologically protectedsurface or edge states at boundaries (1). For the design of the next-generation spintronic devices (2, 3), especially those based on the quan-tum anomalous Hall effect (QAHE), it is crucial to find efficient waysto magnetize their topological surface states (TSSs) while maintain-ing their topological features (4–6). The conventional approach isdoping magnetic ions into TIs (7–11), and the QAHE has been suc-cessfully realized in Cr- or V-doped (Bi, Sb)2Te3 thin films (9–11).However, it is still very challenging to control the distribution and mag-netic order of dopants in TIs, and the critical temperature (Tc) for theobservation of QAHE is extremely low (30 mK) (9). A promising alter-native way to magnetize TSSs is through the interfacial magnetic prox-imity effect by putting three-dimensional (3D) magnetic insulators onTIs (12–18).Unfortunately, the interfacial hybridization inmost of theseheterostructures is too strong, and TSSs are either damaged or shiftedaway from the Fermi level (12, 14, 19). To this end, recently discovered2D-vdW ferromagnetic monolayers (MLs) such as CrI3 (20) appear tooffer an optimal way to magnetize the TSSs of TIs. First, the Curie tem-perature of the CrI3 ML is as high as 45 K (20), and it is hence conceiv-able that the Tc of the QAHE in CrI3/TI heterostructures can be farhigher than that in the Cr-doped (Bi, Sb)2Te3 thin films (9). Further-more, the CrI3 ML is a semiconductor, and thus, the transport proper-ties of TIs should be preserved. Nevertheless, magnetic ions in most2D-vdW magnetic materials such as Cr3+ ions in CrI3 are typicallycovered by nonmagnetic layers in both sides; it is thus questionablewhether their spin polarization can be sensed by TSSs, although thelatter have a fairly large spatial extension.

Here, we report results of systematic computational studies basedon the density functional theory (DFT) that suggest the possibility ofusing a CrI3 ML to magnetize the TSSs of a prototypical 3D TI: Bi2Se3(BS). We build up inversion-symmetric CrI3/BS/CrI3 heterostructureswith a varying thickness for the BS films, from three to seven quintuplelayers (QLs).We find that the TSSs of BS can be effectivelymagnetizedby the CrI3 ML in all cases. However, we show that CrI3/BS/CrI3becomes a Chern insulator only when the BS film is thicker than fiveQLs. This results from the competition between the exchange field

from CrI3 and the remaining interaction between two surfaces of theBS film. This work reveals the subtleness of designing topological spin-tronic materials and provides a general guidance for the realization ofthe QAHE at high temperatures by combining 3D TIs with 2D-vdWmagnetic MLs (20, 21).

RESULTSElectronic properties of CrI3/BS/CrI3 heterostructuresCrI3 ML is a robust 2D semiconducting ferromagnet. It has a perpen-dicular magnetic anisotropy and a reasonably high Curie temperature(45 K) (20). Structurally, CrI6 octahedrons form a honeycomb lattice.The optimized lattice constant of the pristine CrI3 ML is aCrI3 = 7.04 Å,consistent with the previous theoretical result (22). This value is only2.5% smaller than the size of the

ffiffiffi3

p � ffiffiffi3p BS supercell (7.22 Å), andhence, we stretch the CrI3 ML so as to use a manageable unit cell forthe simulation of CrI3/BS/CrI3.We find that all main properties of theCrI3 ML are not substantially affected by the small lattice stretch (seefig. S1 and table S1).

There are three possible highly symmetric alignments between theffiffiffi3

p � ffiffiffi3p BS supercell and the CrI3 ML, i.e., with Cr ions taking theSe, hollow, or Bi sites on BS (Fig. 1A), respectively. The calculatedbinding energies suggest that Cr3+ cations prefer to sit on the top ofSe2− anions (see fig. S2). The optimized interlayer distances betweenthe CrI3 ML and the BS surface are in a range from 3.07 to 3.12 Å,depending on the thickness of the BS film (see fig. S3). Note that theenergy change is very small as we shift the CrI3 ML in the lateral plan,so it is crucial to impose the inversion symmetry during the structuraloptimization. Here, we only discuss electronic and magnetic propertiesof the most stable configuration.

To shed some light on the interaction across the CrI3/BS interface,we plot the charge density difference Dr of CrI3/BS/CrI3, using six-QLBS as an example in Fig. 1B. The charge redistribution only occurswithin a couple of atomic layers in BS, and the magnitude of Dr issmall. In particular, there is no observable net charge transfer be-tween CrI3 and BS. This is understandable since the bandgap of thefreestanding CrI3 ML is rather wide (larger than 1 eV). The inter-facial Se atoms acquire a small but meaningful magnetic momentof −0.003 mB, which aligns antiparallelly with the magnetic momentsof Cr3+ ions. The planar-averaged spin density Ds (Fig. 1C) showsthat the negative spin polarization penetrates through the top half ofthe first QL of BS, following the direction of spin polarization of theiodine atoms.

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The calculated band structures of CrI3/BS/CrI3 with different thick-nesses of BS (four, five, and six QLs) are shown in Fig. 2 (A to C, respec-tively). One important feature is that bands near the Fermi level arepredominantly fromBS, andCrI3 states lie either 0.7 eV above the Fermilevel or at least 0.3 eV below the Fermi level. As a result, the Dirac conefeature of TSSs are well maintained, or more explicitly, (i) all three caseshave bandgaps of several millielectron volts at the G point and (ii) thespin degeneracies of TSSs are lifted, indicating that the TSSs of BS aremagnetized by theCrI3ML. These results suggest the suitability of usingvdWmagneticMLs to realize QAHE, instead of using conventional fer-romagnetic or antiferromagnetic films that damageTSSs (14, 15, 19, 23).

Topological properties of CrI3/BS/CrI3 heterostructuresTo examine whether the magnetized TSSs of BS by CrI3 MLs aretopologically nontrivial, we take CrI3/4QL-BS/CrI3 and CrI3/5QL-BS/CrI3 as examples and calculate their Chern numbersCN by integrat-ing the Berry curvature in the first Brillouin zone with the Wannier90package (see figs. S4 and S5). The Chern numbers of CrI3/4QL-BS/CrI3and CrI3/5QL-BS/CrI3 are C

4QLN ¼ 0 and C5QLN ¼ 1, respectively. This

indicates that the former is a normal insulator but the latter is a Cherninsulator. As shown in Fig. 3A, the QAHE state of CrI3/5QL-BS/CrI3 isfurther confirmed by the presence of one chiral edge state that connectsthe valance and conduction bands.

Hou et al., Sci. Adv. 2019;5 : eaaw1874 31 May 2019

Weuse a low-energy effective four-bandHamiltonian to thoroughlystudy the topological properties of all CrI3/BS/CrI3 films. Note thatstates of CrI3 MLs are far away from the Fermi level and that the effectof CrI3 ML on TSSs of BS can be represented by an exchange field(HZeeman) and an interfacial potential (HInterface). Hence, the low-energy effective four-band Hamiltonian (2, 5, 6) within the basis setof {∣t, ↑ 〉, ∣t, ↓ 〉, ∣b, ↑ 〉, and ∣b, ↓ 〉} is

Hðkx; kyÞ ¼ Hsurfðkx; kyÞ þHZeemanðkx; kyÞ þ HInterfaceðkx; kyÞ0 ivFk� Mk 0

2 3

¼ A kx2 þ ky2

� �þ �ivFkþ 0 0 MkMk 0 0 �ivFk�0 Mk ivFkþ 0

664 775þ

D 0 0 00 �D 0 00 0 D 00 0 0 �D

2664

3775þ

Vp 0 0 00 Vp 0 00 0 �Vp 00 0 0 �Vp

2664

3775 ð1Þ

Here, t and b denote the top and bottom surface states, respectively; ↑and ↓ represent the spin up and down states, respectively; vF andk± = kx ± iky are the Fermi velocity and wave vectors, respectively;

Fig. 1. Atomic structure and charge difference in CrI3/BS/CrI3. (A) Side view of the most stable CrI3/BS/CrI3. The green, red, pink, and blue balls are for I, Cr, Se, andBi atoms, respectively. Dashed lines show the alignments between atoms in CrI3 and BS layers; d0 denotes the optimized vdW gap. (B) Real-space distribution of thecharge difference Dr = rtotal − rBS − rCrI3 and (C) planar-averaged spin density Ds = r↑ − r↓ in the interfacial region of the CrI3/6QL-BS/CrI3 heterostructure.

Fig. 2. Band structures of CrI3/BS/CrI3. DFT-calculated band structures of (A) CrI3/4QL-BS/CrI3, (B) CrI3/5QL-BS/CrI3, and (C) CrI3/6QL-BS/CrI3. Insets in (A), (B), and (C)are the fine band structures around the Fermi level. Colors in the main panels indicate the weights of bands from BS (blue) and CrI3 (yellow). Colors in insets indicate thespin projections.

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andMk =M − B(kx2 + ky

2) describes the coupling between the top andbottomTSSs. Note thatM represents the gap produced by this couplingrather than magnetization as conventionally used, D is the exchangefield from CrI3, and Vp represents the magnitude of the asymmetricinterfacial potential. AlthoughVp vanishes in themodels with inversionsymmetry, the situation in experiments can be changed by the mis-alignment of two CrI3 MLs and by the presence of substrates and coverlayers. Therefore, we keep theVp term to hold the generality of our dis-cussions. As shown in fig. S6 and table S2, the DFT bands of CrI3/BS/CrI3 around the G point can be fitted well by this Hamiltonian, indicat-ing its applicability to these systems. The Berry curvature W(k) andChern number CN are calculated on the basis of the formulas in (24).

There is a clear phase boundary in Fig. 3B for the topological fea-ture of CrI3/BS/CrI3, i.e., CN = 0 (CN = 1), when BS is thinner (thicker)than fiveQLs, consistent with the Chern numbers obtained byWannierfunctions in CrI3/BS/CrI3 with four- and five-QL BS. Therefore, CrI3/BS/CrI3 heterostructures with less than five QLs of BS are normal insu-lators, and five QLs of BS are required to realize the QAHE inexperiments. The calculated bandgaps of CrI3/5QL-BS/CrI3, CrI3/6QL-BS/CrI3, and CrI3/7QL-BS/CrI3 are 2.3 meV (27 K), 3.6 meV(42 K), and 5.9 meV (68 K), respectively. Equation 1 shows that itsbandgap is 2∣M − D∣ (here,M > 0 and D> 0). On the basis of the datain Fig. 3 (C and D), we see that the increase of bandgap with the BSthickness mainly results from the monotonic decrease ofM. Moreover,the nontrivial bandgap of CrI3/BS/CrI3 noticeably increases with the re-duction of d (see the inset in Fig. 3B for CrI3/6QL-BS/CrI3), indicatingthat it is beneficial to make d smaller through an external pressure forthe realization of QAHE. Considering that theMLCrI3 has a Tc of 45 K(20) and no other complex factors, such as uncontrollable distributionof dopants, localmagnetic ordering, and charge transfer, are involved inthese systems, we believe that QAHE should be observable in CrI3/BS/CrI3 heterostructures up to a few tens of kelvins, much higher than thetemperature achieved with the doping approach (9–11).

In general, we find rules that govern topological properties of CrI3/BS/CrI3, i.e., (i) CN = 1 when D

2 > M2 and (ii) CN = 0 when D2 < M2.

This is consistent with the phase diagram in (5) and gives simple waysto manipulate the topological properties of systems with a 2D mag-netic ML on TI. As shown in the Fig. 3C, the exchange field D slightlydepends on the thickness of the BS film and fluctuates around 3.5 meV.

Hou et al., Sci. Adv. 2019;5 : eaaw1874 31 May 2019

This result is understandable since exchange field D mainly dependson the interfacial interaction between CrI3 and BS. As expected,M hasa strong dependence on the thickness of the BS film and exponentiallydecreases as the BS film becomes thicker (Fig. 3D). Note that the verysmall M = 0.5 meV in CrI3/7QL-BS/CrI3 is consistent with the ex-perimentally observed gap closing in BS films thicker than six QLs(25). Since Vp is zero in CrI3/BS/CrI3 films with the inversionsymmetry, the Hamiltonian equation 1 can be rewritten in terms ofthe basis of {∣ + , ↑ 〉, ∣ − , ↓ 〉, ∣ + , ↓ 〉, and ∣ − , ↑ 〉} with ∣±; ↑〉 ¼ð∣t; ↑〉±∣b; ↑〉Þ= ffiffiffi2p and ∣±; ↓〉 ¼ ð∣t; ↓〉±∣b; ↓〉Þ= ffiffiffi2p as (2, 5)

~Hðkx; kyÞ ¼ A kx2 þ ky2� �þ Hþðkx; kyÞ 0

0 H�ðkx; kyÞ� �

ð2Þ

In Eq. 2, H±(kx, ky) = vFkysx ∓ vFkxsy + [M ± D − B(kx2 + ky

2)]sz andsx, y, z are Pauli matrices. From this Hamiltonian, we can get that thecondition of D2 > M2 leads to only one of the band inversions, ei-ther in H+(kx, ky) or in H−(kx, ky), and a Chern number CN =D/∣D∣ (see table S3). This is understandable because the exchangesplitting D can overcome the coupling-induced gap M in this condi-tion and cause the band inversion of a pair of spin subbands (26). InCrI3/BS/CrI3 with four-QL or thinner BS, we have D

2 M2 and hence become topologically nontrivial with CN = 1. Evenin the case that the top and bottom TSSs are completely decoupled,i.e., both M = 0 and B = 0, the exchange field D from the CrI3 MLstill leads to the QAHE in CrI3/BS/CrI3 as a result of the uniquehalf-integer quantum Hall of the 2D massive Dirac Fermion inthe two surfaces of the 3D TI (5, 6, 27).

To explore the effect of inversion symmetry breakdown, we inves-tigate the evolution of band structure of CrI3/6QL-BS/CrI3 as theasymmetric interface potential Vp increases. The original topologicallynontrivial bands (Fig. 4A) gradually change to M- and W-shapedbands (Fig. 4C) for Vp > 2.8 meV. Similar M- and W-shaped bandsinduced by Vp are also reported in a previous work (28). The bottompanel of Fig. 4D shows the Berry curvature of the occupied bands asVp = 5.0 meV. One may see regions with both negative and positiveBerry curvatures around the G point. This is different from the Berry

Fig. 3. Topological properties of CrI3/BS/CrI3. (A) Chiral edge state of the Chern insulator CrI3/5QL-BS/CrI3 ribbon. (B) Dependence of Chern numbers and gaps ofCrI3/BS/CrI3 on the number (N) of QLs of BS. The inset shows the dependence of bandgaps of CrI3/6QL-BS/CrI3 on the CrI3-BS interlayer distance d. d0 is the optimizedinterfacial distance. (C) and (D) show the fitting parameters D and M in different CrI3/BS/CrI3 heterostructures, respectively. The horizontal dashed line in (B) shows theposition of 3.5 meV.

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curvature for the Vp = 0 case shown in the top panel of Fig. 4D, whereonly a huge positive Berry curvature appears. With the presence ofVp, the criterion for the topological phase transition can be extendedas follows (5): (i) When D2 > M2 þ V2p, CN = 1, and (ii) when D2 <M2 þ V2p, CN = 0. Note that it is counterintuitive that M- andW-shapedbands induced by the asymmetric interface potential Vp is topologi-cally trivial. This shows the subtleness of identifying a topological stateof CrI3/BS/CrI3 heterostructures or probably all analogous materialsystems. Note that the presence of Vp quickly reduces the topologicallynontrivial gap in the Chern insulator region (Fig. 4E). This shows theimportance of maintaining the inversion symmetry of CrI3/BS/CrI3heterostructures for the realization of QAHE and other exotic quan-tum properties (26).

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DISCUSSIONMagnetizing TSSs of TIs is of great importance as it gives rise to QAHEandmany other novel phenomena, especially the hallmark of 3D TIs—the topological magnetoelectrical effect (27). We noted that large spinsplitting might be produced in TSSs through d codoping of Mn andSe(Te) in the topmost QL of TIs (29), but this may involve issues re-garding the distribution andmagnetic ordering of dopants. Asmagneticinsulators such asMnSe and EuS damage TSSs or shift TSSs away fromthe Fermi level (12, 14, 19), the emergent 2D-vdWmagneticMLs (20, 21)offer unique opportunities tomagnetize TSSs through the proximity ef-fect as demonstrated in the present work.

In summary, using CrI3/BS/CrI3 heterostructures as modeling sys-tems, we demonstrated that the emergent 2D-vdW magnetic MLs caneffectively magnetize TSSs of TIs and also maintain their topologicalcharacteristics around the Fermi level. Furthermore, our analyses withan effective four-band Hamiltonian verify that CrI3/BS/CrI3 are Cherninsulators when the BS film is five QLs or thicker. Their bandgaps are afew millielectron volts, and we believe that the QAHE is observable inthese heterostructures at a temperature of a few tens of kelvins. As thefamily of 2D-vdWmagnetic MLs steadily expands, it is foreseeable thateven a higher-temperature QAHE can be achieved. According to dis-cussions above, promising 2D-vdW magnetic MLs should have strongmagnetization, large spatial extension of spin density, and shorter inter-facial distance to TI surfaces.

Hou et al., Sci. Adv. 2019;5 : eaaw1874 31 May 2019

MATERIALS AND METHODSWe used the Vienna Ab initio Simulation Package at the level of thegeneralized gradient approximation (30, 31) in this work. The projector-augmented wave pseudopotentials were adopted to describe the core-valence interaction (32, 33), and the energy cutoff for the plane-waveexpansion was set to 500 eV (31). As shown in Fig. 1A, we constructedinversion-symmetric CrI3/BS/CrI3 slab models with a

ffiffiffi3

p � ffiffiffi3p BSsupercell in the lateral plane to match the CrI3 ML. The vacuum spacebetween adjacent slabs was set to 15 Å. Atomic structures were fullyoptimized with a criterion that requires the force on each atom beingless than 0.01 eV/Å. To correctly describe the weak interaction acrossCrI3 and BS layers and the strong relativistic effect in Bi and I atoms, weincluded the nonlocal vdW functional (optB86b-vdW) (34) and thespin-orbit coupling (SOC) term in the self-consistent iterations. Fur-thermore, the local-spin-density approximations plus U (LSDA+U)method (35), with the on-site Coulomb interactionU = 3.0 eV and theexchange interaction J=0.9 eV,was adopted to take the strong correla-tion effect of Cr 3d electrons into account. Topological properties ofCrI3/BS/CrI3 slabs were studied by using effectiveHamiltonians and theWannier90 package (36). Test calculations indicate that the topologicalproperties ofCrI3/BS/CrI3 are very robust against the choices ofU (fig. S7).

SUPPLEMENTARY MATERIALSSupplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaaw1874/DC1Table S1. Magnetic moment, bandgap, magnetocrystalline anisotropy energy, and Heisenbergexchange interactions J1 and J2.Table S2. Parameters of the effective four-band model (see Eq. 1 in the main text) are used tofit the DFT-calculated band of CrI3/BS/CrI3.Table S3. Analysis of band inversions and the Chern number CN with respect to parameters D,M, and B.Fig. S1. DFT + SOC + U–calculated band structure of the CrI3 ML with pristine and stretchedlattice constants.Fig. S2. Top views of the three highly symmetric alignments between CrI3 and BS inCrI3/BS/CrI3 heterostructures.Fig. S3. Dependence of the binding energies and the vdW gaps of CrI3/BS/CrI3 on the number(N) of QL of BS.Fig. S4. Topological properties of CrI3/4QL-BS/CrI3.Fig. S5. Topological properties of CrI3/5QL-BS/CrI3.Fig. S6. DFT-calculated (black lines) and fitted band structures (red dashed lines) of CrI3/BS/CrI3based on the effective four-band model (see Eq. 1 in the main text).Fig. S7. Effect of U on the topological properties of CrI3/BS/CrI3.

Fig. 4. Effect of Vp on the topological properties of CrI3/6QL-BS/CrI3. (A) to (C) show band evolutions with Vp increasing from 0 to 5.0 meV. (D) Berry curvatures ofoccupied bands around the G point for Vp = 0 (A, top) and Vp = 5.0 meV (C, bottom). The large positive Berry curvatures in the bottom panel are highlighted by blackcircles. (E) Dependence of Chern numbers and gaps on Vp D=3.1 meV and M = 1.4 meV are adopted in these calculations.

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Acknowledgments: DFT calculations were performed on parallel computers at NERSC.Funding: Work was supported by DOE-BES (grant no. DE-FG02-05ER46237). Authorcontributions: R.W. conceived the idea of this study. Y.H. performed DFT calculations.J.K. calculated the edge states. Y.H. and R.W. wrote the manuscript. All authors commented onthe manuscript. Competing interests: The authors declare that they have no competinginterests. Data and materials availability: All data needed to evaluate the conclusionsin the paper are present in the paper and/or the Supplementary Materials. Additional datarelated to this paper may be requested from the authors.

Submitted 27 November 2018Accepted 23 April 2019Published 31 May 201910.1126/sciadv.aaw1874

Citation: Y. Hou, J. Kim, R. Wu, Magnetizing topological surface states of Bi2Se3 with a CrI3monolayer. Sci. Adv. 5, eaaw1874 (2019).

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